Control of Ultra-cold Inelastic Collisions by Feshbash Resonances and Quasi-One-Dimensional Confinement

Cold inelastic collisions of atoms or molecules are analyzed using very general arguments. In free space, the deactivation rate can be enhanced or suppressed together with the scattering length of the corresponding elastic collision via a Feshbach resonance, and by interference of deactivation of the closed and open channels. In reduced dimensional geometries, the deactivation rate decreases with decreasing collision energy and does not increase with resonant elastic scattering length. This has broad implications; e.g., stabilization of molecules in a strongly confining two-dimensional optical lattice, since collisional decay of the highly vibrationally excited states due to inelastic collisions is suppressed. The relation of our results with those based on the Lieb-Liniger model are addressed.Comment: 5 pages, 1 figur

Simultaneous minimum-uncertainty measurement of discrete-valued complementary observables

We have made the first experimental demonstration of the simultaneous minimum uncertainty product between two complementary observables for a two-state system (a qubit). A partially entangled two-photon state was used to perform such measurements. Each of the photons carries (partial) information of the initial state thus leaving a room for measurements of two complementary observables on every member in an ensemble.Comment: 4 pages, 4 figures, REVTeX, submitted to PR

Universal Uncertainty Principle in the Measurement Operator Formalism

Heisenberg's uncertainty principle has been understood to set a limitation on measurements; however, the long-standing mathematical formulation established by Heisenberg, Kennard, and Robertson does not allow such an interpretation. Recently, a new relation was found to give a universally valid relation between noise and disturbance in general quantum measurements, and it has become clear that the new relation plays a role of the first principle to derive various quantum limits on measurement and information processing in a unified treatment. This paper examines the above development on the noise-disturbance uncertainty principle in the model-independent approach based on the measurement operator formalism, which is widely accepted to describe a class of generalized measurements in the field of quantum information. We obtain explicit formulas for the noise and disturbance of measurements given by the measurement operators, and show that projective measurements do not satisfy the Heisenberg-type noise-disturbance relation that is typical in the gamma-ray microscope thought experiments. We also show that the disturbance on a Pauli operator of a projective measurement of another Pauli operator constantly equals the square root of 2, and examine how this measurement violates the Heisenberg-type relation but satisfies the new noise-disturbance relation.Comment: 11 pages. Based on the author's invited talk at the 9th International Conference on Squeezed States and Uncertainty Relations (ICSSUR'2005), Besancon, France, May 2-6, 200

Control of quantum interference in the quantum eraser

We have implemented an optical quantum eraser with the aim of studying this phenomenon in the context of state discrimination. An interfering single photon is entangled with another one serving as a which-path marker. As a consequence, the visibility of the interference as well as the which-path information are constrained by the overlap (measured by the inner product) between the which-path marker states, which in a more general situation are non-orthogonal. In order to perform which-path or quantum eraser measurements while analyzing non-orthogonal states, we resort to a probabilistic method for the unambiguous modification of the inner product between the two states of the which-path marker in a discrimination-like process.Comment: Submitted to New Journal of Physics, March 200

Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement

The Heisenberg uncertainty principle states that the product of the noise in a position measurement and the momentum disturbance caused by that measurement should be no less than the limit set by Planck's constant, hbar/2, as demonstrated by Heisenberg's thought experiment using a gamma-ray microscope. Here I show that this common assumption is false: a universally valid trade-off relation between the noise and the disturbance has an additional correlation term, which is redundant when the intervention brought by the measurement is independent of the measured object, but which allows the noise-disturbance product much below Planck's constant when the intervention is dependent. A model of measuring interaction with dependent intervention shows that Heisenberg's lower bound for the noise-disturbance product is violated even by a nearly nondisturbing, precise position measuring instrument. An experimental implementation is also proposed to realize the above model in the context of optical quadrature measurement with currently available linear optical devices.Comment: Revtex, 6 page

Security of quantum cryptography using balanced homodyne detection

In this paper we investigate the security of a quantum cryptographic scheme which utilizes balanced homodyne detection and weak coherent pulse (WCP). The performance of the system is mainly characterized by the intensity of the WCP and postselected threshold. Two of the simplest intercept/resend eavesdropping attacks are analyzed. The secure key gain for a given loss is also discussed in terms of the pulse intensity and threshold.Comment: RevTeX4, 8pages, 7 figure

Complementarity and the uncertainty relations

We formulate a general complementarity relation starting from any Hermitian operator with discrete non-degenerate eigenvalues. We then elucidate the relationship between quantum complementarity and the Heisenberg-Robertson's uncertainty relation. We show that they are intimately connected. Finally we exemplify the general theory with some specific suggested experiments.Comment: 9 pages, 4 figures, REVTeX, uses epsf.sty and multicol.st

Processing and Transmission of Information

Contains research objectives and reports on four research projects.Lincoln Laboratory, Purchase Order DDL-B222Department of the ArmyDepartment of the NavyDepartment of the Air Force under Contract AF19(122)-45

The Standard Model of Quantum Measurement Theory: History and Applications

The standard model of the quantum theory of measurement is based on an interaction Hamiltonian in which the observable-to-be-measured is multiplied with some observable of a probe system. This simple Ansatz has proved extremely fruitful in the development of the foundations of quantum mechanics. While the ensuing type of models has often been argued to be rather artificial, recent advances in quantum optics have demonstrated their prinicpal and practical feasibility. A brief historical review of the standard model together with an outline of its virtues and limitations are presented as an illustration of the mutual inspiration that has always taken place between foundational and experimental research in quantum physics.Comment: 22 pages, to appear in Found. Phys. 199

Timeless path integral for relativistic quantum mechanics

Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all possible paths in the constraint surface specified by the (relativistic) Hamiltonian constraint, and each path contributes with a phase identical to the classical action divided by $\hbar$. The timeless path integral manifests the timeless feature as it is completely independent of the parametrization for paths. For the special case that the Hamiltonian constraint is a quadratic polynomial in momenta, the transition amplitude admits the timeless Feynman's path integral over the (relativistic) configuration space. Meanwhile, the difference between relativistic quantum mechanics and conventional nonrelativistic (with time) quantum mechanics is elaborated on in light of timeless path integral.Comment: 41 pages; more references and comments added; version to appear in CQ